Question

1. -8(p + 2) + p = 4(p + 3) + 5

Explanation:

Step1: Expand the brackets

First, we expand \(-8(p + 2)\) and \(4(p + 3)\) using the distributive property \(a(b + c)=ab+ac\).
For \(-8(p + 2)\), we get \(-8\times p+(-8)\times2=-8p - 16\).
For \(4(p + 3)\), we get \(4\times p+4\times3 = 4p+12\).
So the equation becomes \(-8p - 16 + p=4p + 12 + 5\).

Step2: Combine like terms

On the left - hand side, combine the \(p\) terms: \(-8p + p=-7p\), so the left - hand side is \(-7p-16\).
On the right - hand side, combine the constant terms: \(12 + 5 = 17\), so the right - hand side is \(4p+17\).
Now the equation is \(-7p-16 = 4p+17\).

Step3: Isolate the variable \(p\)

Add \(7p\) to both sides of the equation to get rid of the \(-7p\) on the left:
\(-7p+7p - 16=4p + 7p+17\)
\(-16 = 11p+17\)
Then subtract \(17\) from both sides:
\(-16-17=11p+17 - 17\)
\(-33 = 11p\)

Step4: Solve for \(p\)

Divide both sides by \(11\):
\(p=\frac{-33}{11}=-3\)

Answer:

\(p = - 3\)